Related papers: Jacobi equations and particle accelerator beam dyn…
In a previous article a relationship was established between the linearized metrics of General Relativity associated with geodesics and the Dirac Equation of quantum mechanics. In this paper the extension of that result to arbitrary curves…
Relativistic electromagnetic plasma waves are described by a dynamical equation that can be solved not only in terms of plane waves, but for several different accelerating wavepacket solutions. Depending on the spatial and temporal…
The traditional approach to accelerator optics, based mainly on classical mechanics, is working excellently from the practical point of view. However, from the point of view of curiosity, as well as with a view to explore quantitatively the…
A nonlinear Lorentz invariant kinetic diffusion equation is introduced, which is consistent with the conservation laws of particles number, energy and momentum. The equilibrium solution converges to the Maxwellian density in the Newtonian…
Wave particle duality remains a central interpretational challenge in quantum theory. In this work, we develop a trajectory-based description of photon dynamics formulated in an extended complex space within the relativistic quantum…
A linac (linear accelerator) is a system that allows to accelerate charged particles through a linear trajectory by electromagnetic fields. This kind of accelerator finds several applications in fundamental research and industry. The main…
Relativistic sources, e.g. gamma-ray bursts, pulsar wind nebulae and powerful active galactic nuclei produce relativistic outflows that lead to the formation of collisionless shock waves, where particle acceleration is thought to take…
Employing a suitable nonlinear Lagrange functional, we derive generalized Hamilton-Jacobi equations for dynamical systems subject to linear velocity constraints. As long as a solution of the generalized Hamilton-Jacobi equation exists, the…
The coupling of transverse motion is a natural occurrence in particle accelerators, either in the form of a residual coupling arising from imperfections or originating by design from strong systematic coupling fields. While the first can be…
The relativistic quantum-mechanical description of a charged Laguerre-Gauss beam accelerated in a uniform electric field has been fulfilled. Stationary wave eigenfunctions are rigorously derived. The evolution of the beam parameters during…
A gas of noninteracting particles diffuses in a lattice of pulsating scatterers. In the finite horizon case with bounded distance between collisions and strongly chaotic dynamics, the velocity growth (Fermi acceleration) is well described…
The semiclassical description of the dynamics of wave packets in periodic potentials and subject to an applied force relies on the concepts of effective mass and anomalous transport. This picture is valid if the force changes slowly in time…
We study a class of dynamical systems for which the motions can be described in terms of geodesics on a manifold (ordinary potential models can be cast into this form by means of a conformal map). It is rigorously proven that the geodesic…
A quantum model based on a Euler-Lagrange variational approach is proposed. In analogy with the classical transport, our approach maintain the description of the particle motion in terms of trajectories in a configuration space. Our method…
To improve the presentation we modified the title and used the framework of perturbation modeling of long-term dynamics so as to present the Lorentz-Abraham-Dirac equation as the lowest order, asymptotic differential relation for the…
Everyday experience with centrifugal forces has always guided thinking on the close relationship between gravitational forces and accelerated systems of reference. Once spatial gravitational forces and accelerations are introduced into…
Cubic invariants for two-dimensional Hamiltonian systems are investigated using the Jacobi geometrization procedure. This approach allows for a unified treatment of invariants at both fixed and arbitrary energy. In the geometric picture the…
We propose a semi-classical interpretation of the geometric scalar and vector potentials that arise due to Berry's phase when an atom moves slowly in a light field. Starting from the full quantum Hamiltonian, we turn to a classical…
Wave propagation is a common occurrence in all of physics. A linear approximation provides a simpler way to describe various fields related to observable phenomena in laboratory physics as well as astronomy and cosmology, allowing us to…
Exact solution is obtained for electromagnetic field around a conducting cylinder of infinite length and finite radius, with a periodical axial current, when the wave length is much larger than the radius of the cylinder. The solution…